Mostly the only rap I've been exposed to was the really bad kind. The artists who swear every other word, objectify women, talk about murder and/or cars. That kind of rap I really, really dislike. From the first post, I don't think I like rap in general, just listening to a few of the songs. It's the sound more than the lyrics from those ones.
However, hip hop isn't too bad for occasional listening. The only band I've been able to find that I like is Fort Minor, whose songs I feel convey great messages with good music and vocals.
I'm clueless when it comes to genres, but apparently I stick to the more alternative styles of music (alt. rock, alt. metal, alt. hip hop, etc.) with a bit of indie, post-grunge, and pop-rock mixed in.
Yeah, Fort Minor is pretty awesome. I don't like much of mainstream rap, not nearly as much as i did in high school haha, largely because of the content and the fact that there's no melody! That being said, there are a few rappers that I still listen to and love, and there are some that sing as well.
My favourite rapper is K-Os. He's very alternative, he's philosophical, playing the role of the mystic, and isn't afraid to talk about his emotions. He also sings, raps, and mixes genres very well.
Kid Cudi's also very alternative, because his songs sound like he's off in space. He's the one rapper that I would say sounds least like a rapper.
Mos Def and Black Star (Mos Def & Talib Kweli are Black Star) are actually very talented. Mos Def has got a voice that just seems to roll off every jazzy beat that he uses, giving a real groovy sound.
If you're willing to take the time to listen closely to complex, but crazy lyrics, I'd recommend Lupe Fiasco. He raps about a lot of different things actually, things that actually have some meaning haha. "Shining Down" is a song that I love for the meaning, and "Sunshine" is actually very INFP-friendly
That should get you started

Enjoy!
Oh, and what bands would you recommend in post-grunge and alt-rock? My favourite rock bands are Audioslave, RHCP, Muse and Green Day.